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Three Quantum Algorithms to Solve 3SAT
"... Summary. We propose three quantum algorithms to solve the 3SAT NPcomplete decision problem. The first algorithm builds, for any instance φ of 3SAT, a quantum Fredkin circuit that computes a superposition of all classical evaluations of φ in a given output line. Similarly, the second and third alg ..."
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Summary. We propose three quantum algorithms to solve the 3SAT NPcomplete decision problem. The first algorithm builds, for any instance φ of 3SAT, a quantum Fredkin circuit that computes a superposition of all classical evaluations of φ in a given output line. Similarly, the second and third algorithms compute the same superposition on a given register of a quantum register machine, and as the energy of a given membrane in a quantum P system, respectively. Assuming that a specific non–unitary operator, built using the well known creation and annihilation operators, can be realized as a quantum gate, as an instruction of the quantum register machine, and as a rule of the quantum P system, respectively, we show how to decide whether φ is a positive instance of 3SAT. The construction relies also upon the assumption that an external observer is able to distinguish, as the result of a measurement, between a null and a non–null vector. 1
Energybased Models of P Systems
"... Summary. Energy plays an important role in many theoretical computational models. In this paper we review some results we have obtained in the last few years concerning the computational power of two variants of P systems that manipulate energy while performing their computations: energybased and U ..."
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Summary. Energy plays an important role in many theoretical computational models. In this paper we review some results we have obtained in the last few years concerning the computational power of two variants of P systems that manipulate energy while performing their computations: energybased and UREM P systems. In the former, a fixed amount of energy is associated to each object, and the rules transform objects by manipulating their energy. We show that if we assign local priorities to the rules, then energy–based P systems are as powerful as Turing machines, otherwise they can be simulated by vector addition systems and hence are not universal. We also discuss the simulation of conservative and reversible circuits of Fredkin gates by means of (self)– reversible energy–based P systems. On the other side, UREM P systems are membrane systems in which a given amount of energy is associated to each membrane. The rules transform and move single objects among the regions. When an object crosses a membrane, it may modify the associated energy value. Also in this case, we show that UREM P systems reach the power of Turing machines if we assign a sort of local priorities to the rules, whereas without priorities they characterize the class P sMAT λ, and hence are not universal. 1
IOS Press (Tissue) P Systems with Unit Rules and Energy Assigned to
"... Abstract. We introduce a new variant of membrane systems where the rules are directly assigned to membranes and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. The result of a successful computation is considered to ..."
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Abstract. We introduce a new variant of membrane systems where the rules are directly assigned to membranes and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. The result of a successful computation is considered to be the distribution of energy values carried by the membranes. We show that for systems working in the sequential mode with a kind of priority relation on the rules we already obtain universal computational power. When omitting the priority relation, we obtain a characterization of the family of Parikh sets of languages generated by contextfree matrix grammars. On the other hand, when using the maximally parallel mode, we do not need a priority relation to obtain computational completeness. Finally, we introduce the corresponding model of tissue P systems with energy assigned to the membrane of each cell and objects moving from one cell to another one in the environment as well as being able to change the energy of a cell when entering or leaving the
IOS Press (Tissue) P Systems with Unit Rules and Energy Assigned to
"... Abstract. We introduce a new variant of membrane systems where the rules are directly assigned to membranes and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. The result of a successful computation is considered to ..."
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Abstract. We introduce a new variant of membrane systems where the rules are directly assigned to membranes and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. The result of a successful computation is considered to be the distribution of energy values carried by the membranes. We show that for systems working in the sequential mode with a kind of priority relation on the rules we already obtain universal computational power. When omitting the priority relation, we obtain a characterization of the family of Parikh sets of languages generated by contextfree matrix grammars. On the other hand, when using the maximally parallel mode, we do not need a priority relation to obtain computational completeness. Finally, we introduce the corresponding model of tissue P systems with energy assigned to the membrane of each cell and objects moving from one cell to another one in